Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order

2017 ◽  
Vol 44 ◽  
pp. 304-317 ◽  
Author(s):  
Kolade M. Owolabi
Keyword(s):  
Numerical Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Adaptive Techniques

scholarly journals Solvability of Impulsive Nonlinear Partial Differential Equations with Nonlocal Conditions

2020 ◽  
pp. 140-152
Author(s):  
Ali Kadhim Jabbar ◽  
Sameer Qasim Hasan
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Theoretical Approach ◽  
Nonlinear Partial Differential Equations ◽  
Nonlocal Conditions ◽  
Abstract Cauchy Problem ◽  
Beam Equation ◽  
Partial Differential

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

scholarly journals Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Convergence Analysis ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.

scholarly journals A generalized scheme based on shifted Jacobi polynomials for numerical simulation of coupled systems of multi-term fractional-order partial differential equations

2017 ◽  
Vol 20 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Kamal Shah ◽  
Hammad Khalil ◽  
Rahmat Ali Khan
Keyword(s):  
Numerical Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Jacobi Polynomials ◽  
Initial Conditions ◽  
Coupled Systems ◽  
Operational Matrices ◽  
Partial Differential ◽  
Shifted Jacobi Polynomials

Due to the increasing application of fractional calculus in engineering and biomedical processes, we analyze a new method for the numerical simulation of a large class of coupled systems of fractional-order partial differential equations. In this paper, we study shifted Jacobi polynomials in the case of two variables and develop some new operational matrices of fractional-order integrations as well as fractional-order differentiations. By the use of these operational matrices, we present a new and easy method for solving a generalized class of coupled systems of fractional-order partial differential equations subject to some initial conditions. We convert the system under consideration to a system of easily solvable algebraic equation without discretizing the system, and obtain a highly accurate solution. Also, the proposed method is compared with some other well-known differential transform methods. The proposed method is computer oriented. We useMatLabto perform the necessary calculation. The next two parts will appear soon.

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